A new kinetic theory model of granular flows that incorporates particle stiffness

Granular materials are characterized by large collections of discrete particles of sizes larger than one micron, where the particle-particle interactions are significantly more important than the particle-fluid interactions. These flows can be successfully modeled by the existing Kinetic Theory (KT) models when they are in the dilute regime with low particle-particle collision frequencies, yielding results that agree well with the simulation results of the event-driven hard sphere model or the more sophisticated soft-sphere Discrete Element Method (DEM). However, these KT models become less accurate for granular flows with soft particles (low particle stiffness) at high particle-particle collision frequencies when the predicted collision interval (the time of free flight for a particle prior to the next collision) is comparable to the collision duration; there is a large discrepancy between the results of these KT models and those from the DEM models. In this work we develop a new KT model that could be used to model granular systems of high collision frequencies with a finite particle stiffness. This is done by modifying the fluctuation energy dissipation rate to incorporate the ratio of collision duration to collision interval, a parameter that is determined by both the collision frequency and particle stiffness. We use a linear-spring-dashpot collision scheme to model the elastic potential energy in the system and to uncover the relationship between the constitutive relations of KT and the ratio of collision duration to collision interval.